Actually your resolved command isn't right. It's really this:
ssh -i "~/Keypairs/jadam-macbookpro-ec2-1.pem" "[email protected]"
The double quotes stop the shell expanding ~ and it's treated there as a literal (passed directly on to ssh). Replace it with the environment variable $HOME and the problem will resolve itself:
KEYPAIR="$HOME/Keypairs/jadam-macbookpro-ec2-1.pem"
sudo ssh -i "$KEYPAIR" "$DST" "$REMOTE_SCRIPT"
I should point out that ssh will evaluate the ~ as home directory, but in this case it will be doing so in root's context rather than yours, so will not be looking for the file in your $HOME/.ssh directory.